Abstract：
In the present work, both direct and inverse problems are considered for a Fisher-type fractional diffusion equation, which is proposed to describe the phenomenon of cell migration. For the direct problem, a solution is given via the Fourier method and the Laplace transform. On the other hand, we solved the inverse problem from a Bayesian statistical framework using a set of data that are the result of a cell migration experiment on a wound closure assay. We estimated the parameters of the mathematical model via Markov Chain Monte Carlo methods.
摘要：
在目前的工作中,对于Fisher型分数阶扩散方程，考虑了正反问题，它被提出来描述细胞迁移的现象。对于直接的问题，通过傅立叶方法和拉普拉斯变换给出了一个解。另一方面,我们使用一组数据解决了贝叶斯统计框架中的反问题，这些数据是在伤口闭合试验中进行细胞迁移实验的结果。我们通过马尔可夫链蒙特卡罗方法估计了数学模型的参数。
